We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function f is observed with additive Gaussian white noise. The function f is assumed to have convex support G whose boundary is to be recovered. Rather than directly estimating the intensity function, we develop a procedure which is based on estimating the support function of the set G. This approach is closely related to the method of geometric hyperplane probing, a well-known technique in computer vision applications. We establish bounds that reveal how the estimation accuracy depends on the ill-posedness of the convolution operator and the behavior of the intensity function near the boundary.
Publié le : 2006-06-14
Classification:
Image analysis,
convex sets,
boundary estimation,
deconvolution,
support function,
geometric probing,
rates of convergence,
62G05,
62H35
@article{1152540752,
author = {Goldenshluger, Alexander and Zeevi, Assaf},
title = {Recovering convex boundaries from blurred and noisy observations},
journal = {Ann. Statist.},
volume = {34},
number = {1},
year = {2006},
pages = { 1375-1394},
language = {en},
url = {http://dml.mathdoc.fr/item/1152540752}
}
Goldenshluger, Alexander; Zeevi, Assaf. Recovering convex boundaries from blurred and noisy observations. Ann. Statist., Tome 34 (2006) no. 1, pp. 1375-1394. http://gdmltest.u-ga.fr/item/1152540752/